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March 3, 2019, 1:41 AM GMT

By Phil McCausland and Mariana Atencio

MEXICALI, Mexico — Parents deported to Central America by U.S. immigration officials returned to the southern border Saturday to demand asylum and reunification with the children they were forced to leave behind.

The 29 parents, who were sent back to their home countries last year after crossing illegally into the U.S. with their children, traveled over the past month with immigration lawyers, religious leaders and other supporters in the hope of rejoining their kids.

A father at the border in Mexicali, Mexico, told MSNBC's Mariana Atencio that he waited for seven hours Saturday for information from U.S. immigration officials.

"Time doesn't matter," said the Guatemalan man, who provided only his first name, Neri. "Our love for our child has no price."

The families have 27 children in U.S. custody, and the youngest is 5 years old. Some of the parents have been separated from their kids for nearly a year, said members of private organizations representing the parents. The longest separation is 14 months, they said.

A migrant family walks across a bridge last month in Tijuana, Mexico.Spencer Platt / Getty Images file

Some of the children remain detained while others have been sent to live with foster families or relatives, according to the immigration organizations Al Otro Lado, Families Belong Together and Together Rising.

Sandra Cordero, director of Families Belong Together, said the parents presented themselves for asylum at the port of entry in Mexicali, Mexico, on Saturday, but U.S. Customs and Border Protection told them it had reached capacity and could not allow them to enter the U.S.

"The CBP says they're at capacity," she said. "But they're not giving us information on what that capacity is. We're staying."

Late in the day, Customs and Border Protection began processing the parents' asylum claims, five at a time. The process could mean detention and more delays in possible reunions with their children.

Cordero said in a video that the parents in this group continue to be separated from their children about nine months after they had been told family separations had stopped.

"We know this is not true, so we’re here to reunify them and present them for their legal right to seek asylum,” she said.

The Texas Civil Rights Project, a criminal justice advocacy group, concluded in a report last month that dozens of parents and legal guardians were still separated from their children even after Trump signed the order to end the separation policy.